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The problem involves two functions, \( f(x) = 2x^2 \) and \( g(x) = x + 4 \), and asks for the following:

1. The expression for \( (f + g)(x) \),
2. The expression for \( (f \cdot g)(x) \),
3. The evaluation of \( (f - g)(-2) \).

### Step 1: Finding \( (f + g)(x) \)
By definition, \( (f + g)(x) = f(x) + g(x) \). 

Given:
- \( f(x) = 2x^2 \)
- \( g(x) = x + 4 \)

So:
\[
(f + g)(x) = 2x^2 + (x + 4) = 2x^2 + x + 4
\]

### Step 2: Finding \( (f \cdot g)(x) \)
By definition, \( (f \cdot g)(x) = f(x) \cdot g(x) \).

So:
\[
(f \cdot g)(x) = (2x^2) \cdot (x + 4) = 2x^2(x + 4) = 2x^3 + 8x^2
\]

### Step 3: Evaluating \( (f - g)(-2) \)
By definition, \( (f - g)(x) = f(x) - g(x) \).

So:
\[
(f - g)(x) = 2x^2 - (x + 4) = 2x^2 - x - 4
\]
Now, substitute \( x = -2 \):
\[
(f - g)(-2) = 2(-2)^2 - (-2 + 4) = 2(4) - (2) = 8 - 2 = 6
\]

### Final Answers:
1. \( (f + g)(x) = 2x^2 + x + 4 \)
2. \( (f \cdot g)(x) = 2x^3 + 8x^2 \)
3. \( (f - g)(-2) = 6 \)

Would you like further details on any of the steps?

Here are 5 related questions you might consider:
1. What is \( (f - g)(x) \)?
2. How do you evaluate \( (f \cdot g)(-2) \)?
3. What would the derivative of \( (f + g)(x) \) be?
4. How does the function \( (f \cdot g)(x) \) behave for large values of \( x \)?
5. What happens if you compute \( (f / g)(x) \)?

**Tip**: Always double-check your function evaluations by substituting carefully to avoid simple arithmetic mistakes.

Write the expressions for (f + g)(x) and (f · g)(x) and evaluate (f - g)(-2) for the functions f(x) = 2x^2 and g(x) = x + 4.

Learn how to perform operations on functions such as addition, multiplication, and subtraction with detailed examples. This problem involves the functions f(x) = 2x^2 and g(x) = x + 4, showing step-by-step how to compute (f + g)(x), (f · g)(x), and (f - g)(-2). Suitable for students in Grades 9-10.

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